Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 4x - 8$ and $ BC = 9x - 53$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {4x - 8} = {9x - 53}$ Solve for $x$ $ -5x = -45$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 4({9}) - 8$ $ BC = 9({9}) - 53$ $ AB = 36 - 8$ $ BC = 81 - 53$ $ AB = 28$ $ BC = 28$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {28} + {28}$ $ AC = 56$